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<div class="iris_headline">IRIS Toolbox Reference Manual</div>




<h2 id="tseries/arf">arf</h2>
<div class="headline">Run autoregressive function on a tseries object</div>

<h4 id="syntax">Syntax</h4>
<pre><code>X = arf(X,A,Z,RANGE,...)</code></pre>
<h4 id="input-arguments">Input arguments</h4>
<ul>
<li><p><code>X</code> [ tseries ] - Input data from which initial condition will be taken.</p></li>
<li><p><code>A</code> [ numeric ] - Vector of coefficients of the autoregressive polynomial.</p></li>
<li><p><code>Z</code> [ numeric | tseries ] - Exogenous input or constantn in the autoregressive process.</p></li>
<li><p><code>RANGE</code> [ numeric | Inf ] - Date range on which the new time series observations will be computed; <code>RANGE</code> does not include pre-sample initial condition. <code>Inf</code> means the entire possible range will be used (taking into account the length of pre-sample initial condition needed).</p></li>
</ul>
<h4 id="output-arguments">Output arguments</h4>
<ul>
<li><code>X</code> [ tseries ] - Output data with new observations created by running an autoregressive process described by <code>A</code> and <code>Z</code>.</li>
</ul>
<h4 id="description">Description</h4>
<p>The autoregressive process has one of the following forms:</p>
<pre><code>a1*x + a2*x(-1) + ... + an*x(-n) = z,</code></pre>
<p>or</p>
<pre><code>a1*x + a2*x(+1) + ... + an*x(+n) = z,</code></pre>
<p>depending on whether the range is increasing (running forward in time), or decreasing (running backward in time). The coefficients <code>a1</code>,...<code>an</code> are gathered in the <code>A</code> vector,</p>
<pre><code>A = [a1,a2,...,an].</code></pre>
<h4 id="example">Example</h4>
<p>The following two lines create an autoregressive process constructed from normally distributed residuals,</p>
<p><span class="LaTeX">$$ x_t = \rho x_{t-1} + \epsilon_t $$</span></p>
<pre><code>rho = 0.8;
X = tseries(1:20,@randn);
X = arf(X,[1,-rho],X,2:20);</code></pre>

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<div class="copyright">IRIS Toolbox. Copyright &copy; 2007&#8212;2013 Jaromir Benes.</div>
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